REFERENCES > COHERENCE TABLES > COHERENCE OF PLACE VALUE STRATEGIES

## COHERENCE OF PLACE VALUE STRATEGIES

KINDERGARTEN

GRADE 1

GRADE 2

GRADE 3

GRADE 4

GRADE 5

Compose and decompose numbers 1-20 into tens and ones.

Use strategies for addition and subtraction within 20.

Use strategies to fluently add and subtract within 100.

Fluently multiply and divide by applying properties of operations

Add, subtract, multiply, and divide multi-digit whole numbers.

K.OA.3 K.OA.4

K.NBT.1

1.OA.3 1.OA.4

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5.NF.1 5.NF.2

Decompose numbers less than or equal to 10 into pairs in more than one way by using objects or drawings, and record by a drawing or equation.

For any number from 1 to 9, find the number that makes 10 when added to the given number by using objects or drawings, and record with a drawing or equation.

Compose and decompose numbers from 11 to 19 into ten ones and some further ones by using objects or drawings, and record by a drawing or equation understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

Apply properties of operations using strategies to add and subtract.

Understand subtraction as an unknown-addend problem.

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten decomposing a number leading to a ten using the relationship between addition and subtraction and creating equivalent but easier or known sums.

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Apply properties of operations as strategies to multiply and divide.

Understand division as an unknown-factor problem.

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental

computation and estimation strategies including rounding.

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and

subtraction; relate the strategy to a written method and explain the reasoning used.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions

with like denominators.

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by

using equations, rectangular arrays, and/or area models.

Add, subtract, multiply, and divide whole numbers, fractions, and decimals.

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